Academic literature on the topic 'Numerical model'

Introduction/purpose: To study the adequacy of applying numerical methods in the modal analysis of complex carrying structures of cranes. Methods: Comparative application of the analytical method and the numerical method - FEM. Results: Some comparative values of the modal parameters were obtained both analytically and numerically for the derived solution of a gantry crane carrying structure. Conclusion: It is shown that the numerical method can give a reliable general quality estimate of the structural behaviour of a complex carrying structure from the aspect of modal analysis.

A water hammer can produce severe consequences regarding pipe integrity; simulation thus becomes an essential requirement for ensuring proper water distribution system design and operation. This article thus tries to demonstrate the importance of numerical methods in resolving such problems. A Scilab code allowing pressure propagation to be represented using the characteristics’ method applied to a case of classic literature was thus developed for numerically simulating this phenomenon. This method uses a finite difference scheme for resolving mass and momentum equations. The article presents equations governing the problem from the numerical point of view, the phenomenon’s behavior is analysed and results obtained by the numerical approach (calculating finite differences) are compared to those obtained with Scilab and the theoretical solution.

Thesis (MSc)--Stellenbosch University, 2015.
ENGLISH ABSTRACT: Various numerical modelling software packages are available for predicting moored ship motions and forces. The focus of this study was to validate the numerical models QUAYSIM and WAVESCAT and how these models together form a procedure for predicting moored ship motions and forces under the impact of high and low frequency waves. The validation procedure applied in the study involved numerical modelling of a given physical model situation in which moored ship motions and forces were measured under both high and low frequency wave conditions. A physical model with built-in bathymetry was provided by the Council for Scientific and Industrial Research (CSIR) Hydraulics Laboratory in Stellenbosch. The model consisted of a moored container vessel at a jetty, with various mooring lines and fenders. A JONSWAP spectrum, which combines high and low frequency wave components, was used to simulate wave conditions for the modelling of ship motions. The wave periods and wave heights were measured at observation stations located at specific points in the basin. Other measurements such as those of the forces in the fenders and mooring lines were also determined. A multi-step approach was used to numerically predict the ship motions and forces. Firstly, the coastal processes occurring within the basin, which was set up to simulate the physical model wave behaviour, were measured to calibrate the SWAN Delft3D-WAVE model. The wave heights and periods for the respective observation stations were obtained and compared to the physical model measurements. The Delft3D-FLOW SURFBEAT model was used to calculate the low frequency waves in the coastal area. Low frequency waves are the main cause of larger ship motions and forces, therefore it is important to investigate them as part of the ship motion prediction procedure. After the waves had been computed, wave forces acting on the vessel needed to be determined for both high and low frequency waves. These wave forces were modelled with the combinations SURFBEAT/LF-STRIP (low frequency waves) and SWAN/WAVESCAT (high frequency waves). LF-STRIP provided the link between low frequency wave models and ship motion models, converting the low frequency waves into long wave forces acting on the vessel. WAVESCAT converted the high frequency waves to short wave forces. The calculated long wave forces and short wave forces served as the input required to run the ship motion model QUAYSIM to determine the movements of the moored ship as well as the restraining forces in the lines and fenders. The ship motions and forces were compared to the physical model, with the intention of possibly validating the QUAYSIM/WAVESCAT approach for predicting moored ship motions. The study provides an overview of both the setup and results of the physical and numerical model. A description of each of the numerical models SWAN, SURFBEAT, LF-STRIP, WAVESCAT and QUAYSIM is provided, along with a comparison between the physical and numerical models for each procedure. The validation procedure provided useful documentation of the quality of these numerical modelling approaches, already in use in some design projects. The numerical models WAVESCAT and QUAYSIM models of ship motion have shown to provide a good correlation between the physical model and the numerical approach. However, improvements are still required. Good comparisons were obtained for the long wave motions (horizontal movements - surge, sway and yaw). The surge and sway motions were slightly overestimated by QUAYSIM. The magnitude of the yaw was comparable but the not well represented in spectral plots.
AFRIKAANSE OPSOMMING: Daar is verskeie numeriese modellering-sagtewareprogramme beskikbaar waarmee skipbewegings en -kragte voorspel kan word. Die fokus van hierdie studie was om die numeriese modelle QUAYSIM en WAVESCAT te valideer. Saam vorm hierdie twee modelle ’n prosedure om vasgemeerde skipbewegings en -kragte veroorsaak deur lang- en kortgolfaksie te bepaal. Die validasieprosedure wat in hierdie studie gebruik is, behels ’n numeriese modelering van ’n fisiese situasie waar ’n vasgemeerde skip se bewegings en kragte onder kort- en langgolfkondisies gemeet is. ’n Fisiese model met ingeboude batimetrie is voorsien deur die Council for Scientific and Industrial Research (CSIR) se hidroliese laboratorium in Stellenbosch. Die model bestaan uit ’n vasgemeerde houerskip by ’n pier met verskeie ankerlyne en bootbuffers. ’n JONSWAPspektrum, wat kort- en langgolfkomponente kombineer, is gebruik om golfomstandighede vir die modellering van skipbewegings te simuleer. Golfperiodes en golfhoogtes is by spesifieke waarnemingstasies in die gesimuleerde hawe-area gemeet. Verdere opmetings, soos dié van die kragte in die bootbuffers en ankerlyne, is ook gedoen. ’n Stap-vir-stap benadering is gevolg om die skipbewegings numeries te voorspel. Eerstens is die kusprosesse wat in die gesimuleerde hawe plaasvind, gekalibreer met die numeriese paket SWAN Delft3D-WAVE. Die golfhoogtes en golfperiodes vir elke waarnemingstasie is bereken en vergelyk met die fisiese model se opmetings. Die SURFBEAT-module van Delft3D-FLOW is gebruik om die lae-frekwensie golwe in die kusarea te bereken. Lae-frekwensie golwe is die hoofoorsaak van skipbewegings en daarom is dit belangrik om dit te ondersoek gedurende die voorspellingsprosedure van skipbewegings. Na die golwe bereken is, moes die kragte wat beide kort en lang golwe op die skip uitoefen ook bereken word. Hierdie golfkragte is gemodelleer deur middel van die kombinasies SURFBEAT/LFSTRIP (langgolwe) en SWAN/WAVESCAT (kortgolwe). LF-STRIP het die skakel tussen golfmodelle en skipbewegingsmodelle verskaf en die lae-frekwensie golwe omgeskakel in langgolfkragte wat op die skip uitgeoefen is. WAVESCAT het die hoë-frekwensiegolwe omgeskakel in kortgolfkragte wat op die skip uitgeoefen is. Die berekende langgolf- en kortgolfkragte is ingevoer op die skipbewegingsmodel QUAYSIM om die skipbewegings en inperkingskragte in die bootbuffers en ankerlyne te bepaal sodat dit vergelyk kon word met die fisiese model, met die doel om moontlik die QUAYSIM/WAVESCAT-prosedure om gemeerde skipbewegings te voorspel te valideer. Die studie verskaf ’n oorsig van die opstel en resultate van die fisiese en numeriese modelle. Elk van die numeriese modelle SWAN, SURFBEAT, LF-STRIP, WAVESCAT en QUAYSIM word beskryf en vergelykings word getref tussen die numeriese en fisiese modelle vir elke prosedure. Die validasieprosedure verskaf nuttige dokumentasie van die kwaliteit van hierdie numeriese modeleringsprosedures wat reeds in sekere ontwerpprojekte gebruik word. Die numeriese WAVESCAT en QUAYSIM modelle van skipbewegings het ’n goeie korrelasie tussen die fisiese model en die numeriese benadering gelewer. Verbeteringe is wel steeds nodig. Goeie vergelykings is verkry vir langgolfbewegings (horisontale bewegings – stuwing (“surge”), swaai (“sway”) en gier (“yaw”)). Die stu- en swaaibewegings was effens oorskat met QUAYSIM. Die grootte van die gier was wel vergelykbaar maar is nie grafies goed uitgebeeld nie.

In the present study, a finite volume method is employed to modelthe advection-diffusion phenomenon during a pure substance meltingprocess. The exercise is limited to a benchmark problem consisting ofthe 2D melting from a vertical wall of a PCM driven by natural convectionin the melt. Numerical results, mainly the temporal evolutionof average Nusselt number at the hot wall and the average liquid fraction,are validated by available literature data and the effect of thermalinertia in the heat transfer is considered as well. Finally, motivatedby recent publications and the model presented here, possible new researchtopics are proposed.

In this thesis, we produce a rigorous and quantitative analysis of the errors introduced by finite difference schemes into strong constraint 4D-Variational (4D-Var) data assimilation. Strong constraint 4D-Var data assimilation is a method that solves a particular kind of inverse problem; given a set of observations and a numerical model for a physical system together with a priori information on the initial condition, estimate an improved initial condition for the numerical model, known as the analysis vector. This method has many forms of error affecting the accuracy of the analysis vector, and is derived under the assumption that the numerical model is perfect, when in reality this is not true. Therefore it is important to assess whether this assumption is realistic and if not, how the method should be modified to account for model error. Here we analyse how the errors introduced by finite difference schemes used as the numerical model, affect the accuracy of the analysis vector. Initially the 1D linear advection equation is considered as our physical system. All forms of error, other than those introduced by finite difference schemes, are initially removed. The error introduced by `representative schemes' is considered in terms of numerical dissipation and numerical dispersion. A spectral approach is successfully implemented to analyse the impact on the analysis vector, examining the effects on unresolvable wavenumber components and the l2-norm of the error. Subsequently, a similar also successful analysis is conducted when observation errors are re-introduced to the problem. We then explore how the results can be extended to weak constraint 4D-Var. The 2D linear advection equation is then considered as our physical system, demonstrating how the results from the 1D problem extend to 2D. The linearised shallow water equations extend the problem further, highlighting the difficulties associated with analysing a coupled system of PDEs.

Although only our species has achieved high level of mathematical reasoning, numerical abilities are not a human prerogative and in last decades comparative research showed that several animal species display rudimentary numerical capacities (Agrillo & Beran, 2013). The ability to discriminate between quantities provide multiple benefits in different ecological contexts. For instance, numerical abilities can be useful to select the larger amount of food (Hunt et al., 2008), to reduce the probability of being spotted by predators by getting protection within the largest group of social companions (Cresswell, 1994) and to decide whether attack another group based on the assessment of the relative number of intruders (Benson-Amram et al., 2011). In particular, the discovery in recent years that even simple organisms, such as fish, possess numerical abilities similar to primates has made possible the use of fish as an animal model to study numerical cognition in the absence of language. To date, different studies have shown that fish are able to select the larger shoal of conspecifics (Agrillo et al., 2008) and can be trained to discriminate between groups of figures differing in numerosity both when allowed to use number and continuous quantities and when only number was available (Agrillo et al., 2009, 2010). Fish can also make a spontaneous use of numerical information with apparently the same effort required to discriminate continuous quantities (Dadda et al., 2009). These abilities seem to be partially inborn as one-day old fish are already able to discriminate between small groups of peers (Bisazza et al., 2010). Nonetheless several questions about numerical abilities in fish are still unanswered. For instance, it is unclear whether numerical systems are the same among different species, whether numerical acuity may be affected by different factors, such as cooperation among individuals and the presence of items in motion or whether newborn fish could be trained to discriminate between sets of items. The aim of the present study was to fill this gap. In particular, the first part of the thesis deals with some of the open questions about numerical cognition in adult fish; the second part is focused on the ontogeny of numerical competence. In the first study (Section 4.1) we set up a novel procedure for training fish to discriminate between sets of stimuli (groups of geometrical figures) differing in numerosity as the previous methodology used to train fish was time-consuming, suitable only for social species and potentially stressful for fish. To validate the method, we replicated two published experiments that used operant conditioning to investigate mosquitofish (Gambusia holbrooki) abilities to discriminate between small sets of items and the influence of numerical ratio and total number of figures on large number discrimination (Agrillo et al., 2009, 2010). In the new procedure a pair of stimuli differing in numerosity was introduced at the opposite ends of the experimental tank and a food reward was released in correspondence of the stimulus to be reinforced. Fish were initially trained on an easy numerical ratio (0.5) and were then tested in non-reinforced probe trials for their ability to generalize to new numerosities. The new procedure designed replicated previous results: fish proved able to discriminate up to 2 vs. 3 figures and their performance in the large number range decreased while increasing the numerical ratio though their numerical acuity seemed to have no upper limit. In addition, the new method proved to be rapid, applicable to different fish species and efficient to study discrimination learning in fish in tasks requiring visual stimuli. As a consequence, the novel protocol was adopted in all the training experiments presented in this thesis. The second study (Section 4.2) focused on a potential limit in numerical cognition research: the lack of cross-species studies using the same methodology. The question of whether all vertebrates share the same numerical systems or rather numerical abilities have appeared multiple times during evolution in response to specific selective pressures imposed by the environment, represents one of the main issues of animal cognition. Despite the large number of published data, results are inconsistent because the methodologies adopted vary across studies, making difficult any inter-specific comparison. To date no study has investigated if different fish species have the same numerical systems. This experiment represents the first inter-specific study using the same methodology in fish. Five fish species as diverse as guppies (Poecilia reticulata), zebrafish (Danio rerio), angelfish (Pterophyllum scalare), redtail splitfin (Xenotoca eiseni) and Siamese fighting fish (Betta splendens) were trained on an easy numerical ratio (0.50) and then were compared in their ability to generalize to more difficult ratios (0.67 and 0.75), or to a larger (25 vs. 50) or a smaller (2 vs. 4) total set size. Results showed interesting similarities among the species, opening the possibility of shared numerical systems among phylogenetically distantly related species, more in accord with the existence of ancient quantification systems inherited from a common ancestor than with an independent evolution of numerical abilities in different species. Another important question in the study of numerical cognition concerns the influence of contextual factors on the numerical capacities of a species. It is possible that the performance observed in a numerical task is limited to the specific context in which such abilities are observed rather than reflecting the full numerical competence of a species. To this purpose, the third (Section 5.1) and fourth (Section 5.2) studies investigated the potential influence on fish numerical acuity of factors that normally occur in nature, namely, the cooperative behavior within group and the perception of figures in motion. In natural environment grouping animals interact with each other and these repeated interactions among individuals can affect adaptive response. Recent studies have provided evidence that, in some contexts, collective actions allow to bypass the cognitive limits of a species and to solve problems that go beyond the capacity of a single individual (Krause et al., 2010, Couzin, 2009). To date, all numerical studies in non-human animals have tested subjects individually and it is not known whether collective behavior can enhance the capacity to solve numerical tasks. The third study (Section 5.1) aimed to verify whether fish in dyads were more accurate than single individuals in two different numerical discrimination tasks. In the first task, guppies were required to join the larger group of conspecifics (4 vs. 6); in the second one fish were trained to discriminate between sets of figures (0.5 ratio) and hence were tested in discriminations of increasing difficulty (0.67 and 0.75 ratios). Results showed that dyads performed better than singletons in selecting the larger group of social companions and also made better numerical discriminations of arrays of dots, showing that collective behavior may yield benefits that go beyond the single ecological context. In addition, in both conditions, the better individual of the dyad spontaneously emerged as the leader. Interestingly, the results here obtained aligned with data collected in adult humans where dyadic performance was superior than individual in a collective enumeration task (Bahrami et al., 2013), thus suggesting that cooperation similarly increases numerical acuity in two distantly related species, such as humans and fish. The motion of items is another factor that might potentially affect numerical abilities. Animals are naturally exposed to moving items (e.g., prey, predators) and hence the movement represents a relevant cue in their life. It is known that fish ability to discriminate between small and large groups of conspecifics is differently affected by the quantity of movement of social companions (Agrillo et al., 2008). However it is still unexplored whether fish can discriminate between two-dimensional figures in motion and whether their accuracy is the same in the small and large number range. For example, it has been reported that adult humans are faster and more accurate in estimating small numerosities (≤ 4) of dynamic items than large numerosities (≥ 4), supporting the hypothesis of two distinct numerical systems (Trick et al., 2003, Alston & Humphreys, 2004). To this aim, in the fourth study (Section 5.2) guppies were trained (0.5 ratio) and tested (0.75 ratio) with either static or moving stimuli. We observed a similar effect of items in motion in fish: while a 0.75 ratio was not discriminated with static stimuli in either numerical range (3 vs. 4 and 9 vs. 12), guppies were able to discriminate this ratio with items in motion but only in the small number range (3 vs. 4). To date, comparative psychologists disagree as to whether in non-human species a single system accounts for discriminations over the whole numerical range (called “Approximate number system”), or a distinct system operates over the small number range (≤4) (called “Object tracking system”). Although the results do not represent a direct evidence for the existence of a separate system in the range 1-4, the differential effect of motion reported in guppies reinforces the idea of separate cognitive systems for small and large numbers, in line with data collected in humans. Despite no direct comparisons have been made between fish and humans in this thesis, the similarities between the two species are worth noting as they raise the intriguing possibility that the foundation of our numerical abilities might be evolutionarily more ancient than previously thought, dating back at least as far as the divergence between fish and land vertebrates. The second part of the thesis focused on the development of numerical abilities using newborn guppies as a model species. Developmental studies can provide useful insights with respect to the existence of a single or multiple systems of numerical representation. For instance, exploring developmental trajectories of numerical skills in different contexts can help us to assess whether the same or distinct numerical systems are used in different tasks. Since an adequate method to study discrimination learning in newborn guppies was not available, in the fifth study (Section 6.1) we designed a procedure by taking into account the social needs of young individuals in order to minimize potential stress due to social deprivation, without interfering with the normal development of their behavioral repertoire. We investigated the development of social behavior in the first two weeks of life by using a spontaneous choice task where newborn guppies could choose between social companions and an empty compartment. Then, newborns were given the choice between their own mirror image and a group of peers to assess whether mirrors could be used as a substitute for social companions during experiments. Based on the findings of these experiments, the protocol for discrimination learning in adult fish was adapted to study shape discrimination in newborn fish. Newborn guppies proved capable to learn a simple shape discrimination after few trials and the training method was then used in the last study (Section 6.2) to investigate their numerical competence using sets of two-dimensional objects, as commonly done with adult fish. At present only Bisazza and colleagues (2010) investigated the ontogeny of numerical abilities in fish. The authors found that, at birth, the capacity of guppies to discriminate between shoals differing by one individual included all numerical contrasts in the range 1-4; young guppies proved also be able to discriminate small numerosities by using numerical information only. In Section 6.2 we investigated whether newborns could be trained to discriminate between small sets of figures. To this purpose, we set up three different experimental conditions to study the influence of continuous quantities that co-vary with numbers (cumulative surface area, density, etc.). In the first one number and continuous quantities were simultaneously available, in the second condition only numerical information was available and in the last one, numerical information was made irrelevant (3 vs. 3) and only continuous quantities were available. The result that fish discriminated only very easy numerical contrasts in the range 1-4 when both number and continuous variables were available was in contrast with the results of shoal discrimination experiments (Bisazza et al., 2010) thus suggesting that newborns’ capacity to use number is specific to social stimuli. On the whole data on guppies, both adult fish and newborns, are suggestive of the existence of multiple quantification mechanisms in fish which are domain-specific and serve to solve a limited set of problems in accordance with the hypothesis proposed by different authors (Feigenson et al., 2004; Spelke, 2000). In sum, the data collected in this thesis indicate that even fish, which are provided with a much smaller brain than warm-blooded vertebrates, can discriminate between quantities and solve complex numerical tasks, in line with evidence in other research fields which suggest that processing numerical information might not require complex neural circuits (Hope et al., 2010). This goes together with recent discovery that bony fish possess several other cognitive abilities that were previously believed to be uniquely present in species provided with large, complex brains (i.e. mammalian and avian species) (Bshary et al., 2002). For all these reasons, fish may become a proper model to study cognitive abilities and in particular numerical competence.
Sebbene solamente la nostra specie abbia raggiunto un elevato livello di competenze matematiche, le capacità numeriche non sono una prerogativa umana e negli ultimi decenni la ricerca comparata ha documentato come molte specie animali posseggano rudimentali abilità numeriche (Agrillo & Beran, 2013). La capacità di saper discriminare tra diverse quantità risulta essere vantaggiosa in diversi contesti ecologici. Per esempio, tale abilità può essere utile per scegliere la quantità maggiore di cibo (Hunt et al., 2008), per ridurre la probabilità di essere predati - ottenendo protezione dal gruppo di conspecifici più numeroso (Cresswell, 1994) - e per decidere se intraprendere interazioni aggressive contro un altro gruppo in base al numero di potenziali rivali (Benson-Amram et al., 2011). In particolare, la recente scoperta che persino organismi semplici, come i pesci, posseggono abilità numeriche simili a quelle osservate nei primati ha reso possibile l'utilizzo dei pesci come modello animale per studiare la cognizione numerica in assenza del linguaggio. Ad oggi, diversi studi hanno infatti dimostrato che i pesci sono capaci di selezionare il gruppo di conspecifici più numeroso (Agrillo et al., 2008) e possono essere addestrati a discriminare tra gruppi di figure di diversa numerosità, sia quando possono utilizzare l’informazione numerica e le variabili continue simultaneamente, sia nel caso in cui sia disponibile solamente l’informazione numerica (Agrillo et al., 2009, 2010). È stato inoltre dimostrato che i pesci sono in grado di discriminare tra quantità usando spontaneamente il numero, apparentemente con lo stesso sforzo cognitive richiesto per discriminare le variabili continue (Dadda et al., 2009). Queste capacità sembrano essere in parte innate, dal momento che gli avannotti di un giorno di vita sono già in grado di discriminare tra piccoli gruppi di conspecifici (Bisazza et al., 2010). Tuttavia diverse domande sulle abilità numeriche nei pesci sono ancora senza risposta. Ad esempio, non è chiaro se i sistemi numerici siano gli stessi fra specie differenti, se l'acuità numerica possa essere influenzata da diversi fattori, come la cooperazione tra gli individui e la presenza di oggetti in movimento o se i pesci appena nati possano essere addestrati a discriminare tra gruppi di oggetti bidimensionali. Lo scopo della presente tesi è stato pertanto quello di colmare queste lacune. In particolare, la prima parte della tesi affronta alcune delle questioni aperte sulla cognizione numerica nei pesci adulti, mentre la seconda parte è focalizzata sull’ontogenesi delle abilità numeriche. Nel primo lavoro (Sezione 4.1) è stata messa a punto una nuova procedura per addestrare i pesci a discriminare tra stimoli bidimensionali (gruppi di figure geometriche) di diversa numerosità, dal momento che il metodo precedentemente utilizzato in letteratura richiedeva tempi prolungati, era adatto solo per le specie sociali ed era potenzialmente stressante per i pesci. Per verificare la validità del metodo, sono stati replicati due esperimenti che hanno usato la procedura del condizionamento operante per indagare le capacità della gambusia (Gambusia holbrooki) di discriminare tra piccole numerosità e l’influenza del rapporto numerico e del numero totale di elementi nella discriminazione di grandi quantità (Agrillo et al., 2009, 2010). Nella nuova procedura, veniva introdotta una coppia di stimoli di diversa numerosità alle estremità della vasca sperimentale e successivamente veniva rilasciato del cibo in corrispondenza dello stimolo da rinforzare. I pesci sono stati inizialmente addestrati a distinguere un rapporto numerico relativamente semplice (0.5); successivamente nella fase di test, sono stati sottoposti a delle prove in estinzione (non veniva fornito il rinforzo alimentare) per verificare la loro capacità di generalizzare a nuove numerosità. La nuova procedura messa a punto ha replicato i risultati ottenuti con quella precedentemente utilizzata: i soggetti sono stati in grado di discriminare fino a 2 figure da 3; in presenza di grandi numerosità la prestazione diminuiva all’aumentare del rapporto numerico sebbene la loro capacità di discriminare sembri non avere un limite superiore. Il nuovo metodo si è inoltre rivelato rapido per la raccolta dei dati, applicabile a diverse specie di pesci ed efficacie per studiare l'apprendimento discriminativo in compiti che richiedono stimoli visivi. Di conseguenza, il nuovo protocollo è stato adottato in tutti gli esperimenti presentati in questa tesi che hanno usato la procedura di addestramento. Il secondo lavoro (Sezione 4.2) è incentrato su un potenziale limite della ricerca sulla cognizione numerica: la mancanza di studi inter-specifici che utilizzano la stessa metodologia. La questione se tutti i vertebrati condividano gli stessi sistemi numerici o se piuttosto le abilità numeriche siano apparse più volte durante l'evoluzione in risposta a specifiche pressioni selettive imposte dall'ambiente rappresenta uno dei temi principali della cognizione animale. Nonostante l’elevato numero di dati pubblicati, i risultati non sono coerenti dal momento che sono state utilizzate diverse metodologie di ricerca rendendo così difficile un confronto inter-specifico accurato. Ad oggi, nessuno studio ha indagato se diverse specie di pesci possiedano gli stessi sistemi numerici. Questo lavoro rappresenta il primo studio inter-specifico che utilizza la stessa metodologia nei pesci. Cinque diverse specie, la pecilia (Poecilia reticulata), lo zebrafish (Danio rerio), il pesce scalare (Pterophyllum scalare), la xenotoca (Xenotoca eiseni) ed il pesce combattente (Betta splendens), sono state inizialmente addestrate utilizzando un rapporto numerico semplice (0.50) e successivamente è stata confrontata la loro capacità di generalizzare a rapporti più difficili (0.67 e 0.75) o ad una numerosità maggiore (25 vs. 50) o minore (2 vs. 4). I risultati hanno mostrato interessanti somiglianze tra le specie, suggerendo la possibilità di sistemi numerici condivisi tra specie filogeneticamente distanti tra loro, più in accordo con l’esistenza di antichi sistemi di quantificazione ereditati da un antenato comune piuttosto che con un’evoluzione indipendente delle abilità numeriche in specie diverse. Un'altra questione importante nello studio della cognizione numerica riguarda l'influenza di fattori contestuali sulle capacità numeriche di una specie. È possibile che la prestazione osservata in un compito numerico sia limitata al contesto specifico in cui tali capacità sono state osservate piuttosto che riflettere le reali abilità numeriche della specie. Per questo motivo, il terzo (Sezione 5.1) e il quarto (Sezione 5.2) lavoro hanno studiato la potenziale influenza sull’accuratezza numerica dei pesci di fattori che normalmente si verificano in natura: il comportamento cooperativo all'interno del gruppo e la percezione di figure in movimento. In natura, gli animali che vivono in gruppo interagiscono tra di loro e queste interazioni ripetute tra gli individui possono incidere sulle scelte fatte in diversi contesti. Studi recenti hanno dimostrato che in alcune circostanze le azioni collettive permettono di aggirare i limiti cognitivi di una specie e di risolvere i problemi che vanno al di là delle capacità del singolo individuo (Krause et al., 2010, Couzin, 2009). Fino ad oggi, tutti gli studi di cognizione numerica condotti negli animali hanno preso in considerazione le prestazioni di singoli soggetti e non si sa quindi se il comportamento collettivo possa migliorare la capacità di risolvere compiti di discriminazione numerica. Lo scopo del terzo lavoro (Sezione 5.1) è stato quello di verificare se i pesci sottoposti a test in coppia fossero più accurati rispetto ai soggetti sottoposti a test individualmente in due diversi compiti di discriminazione numerica. Nel primo compito si è osservata la capacità delle pecilie di scegliere il gruppo di conspecifici più numeroso (4 vs. 6); nel secondo, invece, i pesci sono stati addestrati a discriminare tra gruppi di figure con un rapporto numerico pari a 0.5 e successivamente sono stati sottoposti a test usando confronti numerici più difficili (con rapporti pari a 0.67 e 0.75). I risultati hanno mostrato che i soggetti in coppia hanno avuto una prestazione migliore rispetto ai singoli, sia nella scelta del gruppo di conspecifici più numeroso, sia nel compito di discriminazione numerica, dimostrando quindi che il comportamento collettivo può fornire benefici che vanno al di là del singolo contesto ecologico. Inoltre, in entrambe le condizioni, il soggetto più accurato all’interno della coppia nella risoluzione del compito è emerso spontaneamente come leader. È interessante notare che i risultati ottenuti in questo lavoro sono in linea con i dati raccolti negli esseri umani adulti in cui la prestazione dei partecipanti in coppia è risultata superiore rispetto alle prestazioni individuali in un compito collettivo di discriminazione numerica (Bahrami et al., 2013). Questi dati suggeriscono quindi che la cooperazione aumenti l'acuità numerica in maniera simile in due specie filogeneticamente distanti tra di loro: gli esseri umani ed i pesci. Il movimento degli oggetti è un altro fattore che potrebbe potenzialmente influenzare l’acuità numerica. Gli animali sono infatti naturalmente esposti a degli elementi che si muovono (es. prede, predatori) e quindi il movimento rappresenta un segnale saliente nella loro vita. È stato dimostrato che la quantità di movimento dei conspecifici influenza in maniera differente la capacità dei pesci di discriminare tra piccoli (≤ 4) e grandi (≥ 4) gruppi di compagni sociali (Agrillo et al., 2008). Tuttavia non è stato ancora indagato se i pesci siano in grado di discriminare tra figure bidimensionali in movimento e se la loro accuratezza sia la stessa in presenza di piccole e grandi numerosità. Ad esempio, si è osservato che gli esseri umani adulti sono più veloci e più accurati nello stimare piccole quantità ( ≤ 4 ) di elementi in movimento piuttosto che grandi numerosità ( ≥ 4 ), supportando l'ipotesi di due sistemi numerici distinti (Trick et al., 2003, Alston & Humphreys, 2004). A tal fine, nel quarto lavoro (Sezione 5.2) esemplari di pecilia sono stati addestrati (con rapporto numerico 0.5) e sottoposti a test (con rapporto 0.67) con stimoli statici o in movimento. Si è osservato che gli elementi in movimento avevano un effetto simile a quello riportato nella nostra specie: mentre i soggetti a cui erano stati presentati gli stimoli statici non sono stati in grado di discriminate il rapporto pari a 0.67, sia in presenza di piccole che di grandi numerosità (3 vs. 4 e 9 vs. 12), i soggetti a cui erano stati presentati gli stimoli in movimento hanno saputo discriminare questo rapporto ma solo in presenza di piccole numerosità (3 vs 4). Ad oggi, nell’ambito della psicologia comparata c’è un dibattito sul fatto che gli animali posseggano un unico sistema di discriminazione per tutta la scala numerica (chiamato “Approximate number system”), oppure posseggano anche un sistema distinto coinvolto solo nella discriminazione di piccole numerosità (≤ 4) (chiamato “Object tracking system”). Sebbene i risultati ottenuti non rappresentino una prova diretta dell'esistenza di un sistema separato per la discriminazione numerica nell'intervallo 1-4 , il fatto che il movimento influenzi in maniera differente la discriminazione di piccole e grandi quantità nelle pecilie rafforza l'idea di sistemi cognitivi separati per piccoli e grandi numeri, in linea con i dati raccolti negli esseri umani. Nonostante in questa tesi non siano stati effettuati confronti diretti tra pesci e umani, è interessante notare le somiglianze osservate tra le due specie in quanto sollevano la possibilità che le nostre abilità numeriche abbiano un’origine più antica di quanto si pensi, che risalirebbe alla divergenza tra la linea evolutiva dei pesci e quella dei vertebrati terrestri . La seconda parte della tesi è incentrata sullo sviluppo delle abilità numeriche utilizzando gli avannotti di pecilia come specie modello. Gli studi sullo sviluppo delle abilità cognitive possono fornire indicazioni utili per quanto riguarda l'esistenza di un unico o più sistemi di rappresentazione numerica. Ad esempio, studiare lo sviluppo delle capacità numeriche in contesti diversi può aiutarci a capire se gli stessi sistemi numerici sono utilizzati in compiti diversi o piuttosto se vengono usati sistemi differenti. Dal momento che in letteratura non è presente un metodo adeguato per studiare l'apprendimento discriminativo in esemplari giovani di pecilia, nel quinto lavoro (Sezione 6.1) abbiamo messo a punto una procedura tenendo conto delle esigenze sociali dei giovani individui, al fine di ridurre al minimo il potenziale stress dovuto alla deprivazione sociale, senza interferire con il normale sviluppo del loro repertorio comportamentale. Pertanto, inizialmente abbiamo studiato lo sviluppo del comportamento sociale nelle prime due settimane di vita utilizzando un test di scelta spontanea dove gli avannotti potevano scegliere tra un compartimento contenente dei compagni sociali e uno compartimento vuoto. Successivamente veniva data ai giovani soggetti la possibilità di scegliere tra la propria immagine riflessa e un gruppo di coetanei per valutare se gli specchi potessero essere usati come sostituto dei compagni sociali durante gli esperimenti. Sulla base dei risultati ottenuti, è stato adattato il protocollo per l'apprendimento discriminativo usato nei pesci adulti per studiare la capacità degli avannotti di discriminare tra figure. I soggetti si sono dimostrati in grado di imparare una semplice discriminazione tra figure geometriche dopo poche prove; il metodo di addestramento è stato allora utilizzato nell’ultimo lavoro (Sezione 6.2) per studiare le loro capacità numeriche usando insiemi di figure bidimensionali, come viene comunemente fatto con i pesci adulti. Ad oggi, solamente Bisazza e collaboratori (2010) hanno studiato lo sviluppo ontogenetico delle abilità numeriche nei pesci. Gli autori hanno dimostrato che la capacità alla nascita delle pecilie di discriminare tra gruppi di conspecifici di diversa numerosità include tutti i confronti numerici nell’intervallo 1-4; i giovani soggetti hanno dimostrato inoltre di sapere discriminare piccole numerosità usando solamente l’informazione numerica. Nella Sezione 6.2 si è andato a verificare se gli avannotti di pecilia possono essere addestrati a discriminare tra insiemi di figure. A tal fine, sono state messe a punto tre condizioni sperimentali per studiare l'influenza delle variabili continue che co-variano con la numerosità (area complessiva degli stimoli, densità, ecc.). Nella prima condizione sia il numero che le variabili continue erano simultaneamente disponibili, nella seconda, solo l’informazione numerica era disponibile e, nell’ultima condizione l’informazione numerica è stata resa irrilevante (3 vs. 3) ed erano disponibili solo le variabili continue. Il risultato che i soggetti hanno saputo discriminare solo i confronti numerici facili nell’intervallo 1-4 quando sia il numero che le variabili continue erano disponibili è in contrasto con i dati ottenuti negli esperimenti di scelta spontanea (Bisazza et al., 2010), suggerendo che la capacità dei giovani pesci di utilizzare l’informazione numerica sia limitata agli stimoli sociali. Nel complesso i dati raccolti nella pecilia, sia in soggetti adulti che negli avannotti, suggeriscono l'esistenza nei pesci di molteplici meccanismi di discriminazione di quantità coinvolti nella risoluzione di problemi specifici, in accordo con l’ipotesi proposta in precedenza da diversi autori (Feigenson et al., 2004; Spelke, 2000). In sintesi, i dati raccolti in questa tesi indicano che anche i pesci, pur essendo dotati di un cervello molto più piccolo dei vertebrati a sangue caldo, possono discriminare tra quantità e risolvere compiti numerici complessi, in linea con altri ambiti di ricerca che suggeriscono come l’elaborazione dell’informazione numerica potrebbe non richiedere circuiti neurali complessi (Hope et al., 2010). Questo va di pari passo con la recente scoperta che i teleostei possiedono diverse abilità cognitive che in precedenza si ritenevano essere unicamente presenti nelle specie dotate di cervelli più grandi e complessi (es: mammiferi e specie di uccelli) (Bshary et al., 2002). Alla luce dei risultati presentati in questa tesi, è possibile affermare che i pesci costituiscono un modello adeguato per lo studio delle capacità cognitive ed in particolare di quelle numeriche.

Beneath many glaciers and ice sheets, hydrology influences or controls a variety of basal processes. Glaciohydraulic supercooling is a process whereby water freezes englacially or subglacially because its internal temperature is below the bulk freezing temperature. Water supercools when it is at its freezing point and flows from an area of higher pressure (lower ambient temperature) to an area of lower pressure (higher ambient temperature) without equilibrating its internal energy. The process is dependent on the configuration of the water flow path relative to the pressure gradient driving flow. I formulate the governing equations of mass, linear momentum, and internal energy for time-dependent clear water flow based on previous work (Clarke, 2003; Spring & Hutter, 1981, 1982). Because field evidence and steady-state theory point to water distributing laterally across the bed, I modify this theory to account for an aperture that is much wider than deep, which I refer to as a sheet. Ice accretion terms are formulated with porosity because accreting ice has residual porosity. Ice intrusion into such a water sheet is not described in the literature, and I formulate intrusion based on previous work as well as ideas gained from subglacial cavity formation. In addition, I modify the clear water equations to include erosion and deposition of sediment along the glacier bed and incorporation of sediment into the accreted ice. Furthermore, water may leave the ice-bed interface and flow through the glacier pore space because subglacial water pressure is relatively high when supercooling occurs. To this end, I develop an englacial waterflow model that incorporates changes in ice porosity based on creep closure and ice melt or accretion. Simulations reveal behavior that cannot be inferred from simplified models. For example, while total ice accretion is comparable to field estimates, locations of simulated ice accretion along the ice-bed interface conflict with steady state models, which tend to overpredict accretion amounts. Simulations also indicate that much sediment deposition occurs prior to water being supercooled. Sediment deposition tends to smooth subglacial topography rather than enhance it. Additional results and implications of numerical simulations are discussed.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate

The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work, the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances, a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.

Sedimenting suspensions exist in a varity of natural phenomena and industrial applications. It is already observed in experiments that the dilute fibre suspensions experience a concentration instability under gravity at low Reynolds numbers. Initially well-mixed suspensions become inhomogeneous and anisotropic due to this instability. This project is focused on the development and validation of numerical models to understand the instability in a dilute fibre suspension by means of the mixture model and the point-particle model. For periodic boundary condition, we use a linear stability analysis to show that inertia and hydro dynamic translational diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. However, numerical simulations indicate a weak wavenumber selection even at zero Reynolds number. Numerical simulations also show that the induced flow may either die or saturate on a finite amplitude. The characterof this long time behaviour is dictated by the wavenumber, the presence or absence of the translational diusivity, rotational diffusivity, and the fluid inertia on particle motions. Moreover, the most unstable wavenumber decreases with time and the maximum amplitude increases. The smallest wavenumber obtains the largest amplitude at steady state. For a vessel bounded by sidewalls, the near-wall convection is an upward back flow in the very beginning, due to the combined effects of the steric-depleted layer and a hydrodynamiclly-depleted region near the wall. However, the evolution of the near-wall convection at later times depends on the aspect ratio of the bres, the translational diffusivity and the initial perturbations. The steric-depleted layer in the mixture model can be neglected for large widths. Multiple streamers are obtained due to the sidewalls, implying that the sidewalls can generate a wavelength which is smaller than the channel width. The suspension ends up with a single streamer on one side of the container, consistent with the results of the cases with periodic boundary condition but different from the experimental results. This might be due to the absence of the botton wall in the mixture model. Moreover, the global structure evolution of a suspension is dependent on the width of the vessel and the amplitude ofthe initial perturbations.

QC 20140207

Massive stars usually form groups such as OB associations. Their fast stellar winds sweep up collectively the surrounding insterstellar medium (ISM) to generate superbubbles. Observations suggest that superbubble evolution on the surrounding ISM can be very irregular. Numerical simulations considering these conditions could help to understand the evolution of these superbubbles and to clarify the dynamics of these objects as well as the difference between observed X-ray luminosities and the predicted ones by the standard model (Weaver et al. 1977).

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric and Planetary Sciences, 1985.
Microfiche copy available in Archives and Science.
Bibliography: leaves 80-81.
by Haim Nelken.
M.S.

The textbook covers the basics of classical numerical methods of computational mathematics used for solving linear and nonlinear equations and systems; interpolation and approximation of functions; numerical integration and differentiation; solutions of ordinary differential equations by methods of one-dimensional and multidimensional optimization. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for students of higher educational institutions studying in the discipline "Numerical methods".

The Brunswick area consists of many acres of estuarine and marsh environments. The US Army Corps of Engineers District, Savannah, requested that the US Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, develop a validated Adaptive Hydraulics model and assist in using it to perform hydrodynamic modeling of proposed navigation channel modifications. The modeling results are necessary to provide data for ship simulation. The model setup and validation are presented here.

The Houston Ship Channel (HSC) is one of the busiest deep-draft navigation channels in the United States and must be able to accommodate increasing vessel sizes. The US Army Corps of Engineers, Galveston District (SWG), requested the US Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, update and revalidate a previously developed three-dimensional Adaptive Hydraulics (AdH) hydrodynamic and sediment model of the HSC, Galveston, and Trinity Bays. The model is necessary for analyzing potential impacts on salinity, sediment, and hydrodynamics due to alternatives designed to reduce shoaling in the HSC. SWG requested an updated validation of the previously developed AdH model of this area to calendar years 2010 and 2017, utilizing newly collected sediment data. Updated model inputs were supplied for riverine suspended sediment loads as well as for the ocean tidal boundary condition. The updated model shows good agreement to field data in most conditions but also indicates potential issues with freshwater flow inputs as well as the ocean salinity boundary condition.

The overall objective was to develop two models for determining the effect of mechanical damage on the structural integrity of buried pipelines. The models that are to be developed are the instantaneous failure model (MD4-3) and the delayed failure model (MD4-4). The subject of this report is part of the work that has been undertaken in support of the development of the instantaneous failure model which is being undertaken within the remit of MD4-3. The overall objective of MD4-3 to produce a closed form expression that will be used as: (i) A Limit State Function in structural reliability and risk assessment methodologies and associated software. (ii) A means of determining the safety margin associated with known existing damage to establish whether immediate repair is required (iii) An initial condition for the delayed failure model (MD4-4) which is being developed separately. The objective of this report is to present the outcomes of detailed numerical simulation of physical tests that have been performed as part of MD4-1. The development is progressing based on a combination of physical testing and numerical simulation and analysis. The objective of this report is to present the outcomes of detailed numerical simulation of physical tests that have been performed as part of MD4-1.